Date: Mar 15, 2013 6:06 PM
Author: Virgil
Subject: Re: Matheology � 224
In article

<37f8b921-a2db-46d0-a942-2d2ae5b727a3@k14g2000vbv.googlegroups.com>,

William Hughes <wpihughes@gmail.com> wrote:

> On Mar 14, 10:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> <snip>

>

> >... consider the list of finite initial segments of natural numbers

> >

> > 1

> > 1, 2

> > 1, 2, 3

> > ...

> >

> > According to set theory it contains all aleph_0 natural numbers in its

> > lines. But is does not contain a line containing all natural numbers.

> > Therefore it must be claimed that more than one line is required to

> > contain all natural numbers. This means at least two line are

> > necessary. There are no special lines necessary, but there must be at

> > least two. In this case, however, we can prove, by the construction of

> > the list, that every union of a pair of lines is contained in one of

> > the lines. This contradicts the assertion that all natural numbers

> > exist and are in lines of the list.

>

>

> Nope.

>

> Nope, two lines are necessary but not sufficient.

>

> Two lines can never do a better job than 1.

>

> Any finite number of lines is necessary but not sufficient.

>

> Any finite number of lines can never do a better job than 1.

>

> An infinite number of lines is necessary and sufficient

>

> An infinite number of lines can do a better job than 1

>

> [In potential infinity things go

>

> Any number of findable lines is not sufficient

>

> An unfindable line is necessary and sufficient

>

> An unfindable line can do a better job than

> any number of findable lines.

Or it would if you could find it.

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